• Journal of Korean Society of Coastal and Ocean Engineers
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• v.11 no.4
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• pp.197-200
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• 1999

An extension of the modified leap-frog scheme is made to solve the nonlinear shallow-water equations. In the extended model. the physical dispersion of the Boussinesq equations is replaced by the numerical dispersion resulted from the leap-frog finite difference scheme. The model is used to simulate propagations of a solitary wave over a constant water depth and a linearly varying water depth. Obtained numerical results are compared with available analytical and other numerical solutions. A reasonable agreement is observed.

• Proceedings of the Korea Water Resources Association Conference
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• 2007.05a
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• pp.576-580
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• 2007

수치기법이 복잡한 Boussinesq 방정식 대신 간단한 선형 Boussinesq 형태의 파동방정식을 지배방정식으로 사용하면서도 완변수심상 지진해일 전파시 요구되는 물리적 분산효과를 정도 높게 고려할 수 있는 분산보정 지진해일 전파 유한요소모형을 개발하였다. 수심이 변하는 지형에서의 분산보정능력을 검증하기 위해 수중 원형천퇴상을 전파하는 Gaussian 형상의 가상지진에 대해 수치모의를 수행하고, 그 결과를 선형 Boussinesq 방정식에 의해 계산된 수치해와 비교하였다. 그 결과 개발된 유한요소모형이 수심이 변하는 지형에서도 상당히 정확하다는 것이 입증되었다.

• Journal of Korea Water Resources Association
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• v.32 no.4
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• pp.447-455
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• 1999

In this study, the Bragg resonant of cnoidal waves propagating over a sinusoidally varying topography lying on a uniformly sloping beach is investigated. The governing equations derived from the Boussinesq equations are numerically integrated. The effects of fast varying terms and nonlinearity in reflection coefficients are also examined. Variation of reflection coefficient for different sloping beaches is studied. It is found that reflection coefficients are not strongly dependent on slopes of beaches.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.35 no.5
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• pp.1061-1071
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• 2015

In the present study, the Navier-Stokes (N-S) equations delineating water flows inside porous media were derived applying Reynolds transport theorem in order to provide a basis for analyzing water wave problems inside the porous media. Then, the derived N-S equations were compared with the same species of equations in existing researches. Based on the N-S equations, a set of Boussinesq equations was then derived in such a form that the dispersiveness and nonlinearity of water waves inside the porous media can be properly reproduced. Finally, numerical analyses were carried out to demonstrate the validity of the equations. The reflection and transmission coefficients of porous breakwaters were calculated and compared with the results of existing hydraulic experiments. The numerical results showed a rather sensitive dependency on the virtual mass coefficient of grains constituting the porous media. The selection of the coefficient with zero turned out to give nice agreements with numerical and experimental results.

• Proceedings of the Korea Water Resources Association Conference
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• 2005.05b
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• pp.527-531
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• 2005

지진해일파는 풍파에 비해 파장이 매우 길어 장파로 간주되지만 조석에 비하면 파장이 짧아 상대적으로 분산성이 강하므로, 먼거리를 전파하는 경우에는 분산성을 고려하여 해석하여야 한다. 특히 동해에서 발생하는 지진해일의 경우 파원이 작고 수심이 깊어 단주기파 성분이 강하므로 그 물리적인 분산효과가 매우 중요하다. 이에 본 연구에서는 지진해일 수치모의시 임의로 구성된 유한요소망과 양해법을 사용하면서도 복잡한 Boussinesq 방정식 대신 간단한 Boussinesq-type의 파동방정식을 사용하면서도 물리적 분산효과를 정도 높게 고려할 수 있는 능동적인 분산보정기법을 이용한 2차원 유한요소모형을 개발하여 가상진원에 의해 발생된 2차원 지진해일 전파에 대하여 수치모의한 결과, 요소크기와 시간간격이 고정되었음에도 불구하고 다양한 수심에 대해 선형 Boussinesq 방정식의 해석해와 매우 잘 일치하는 좋은 결과를 보였다.

• Proceedings of the Korea Water Resources Association Conference
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• 2007.05a
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• pp.2130-2134
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• 2007

선형 Boussinesq 형태의 파동방정식을 지배방정식으로 사용하는 능동적인 분산보정 지진해일 전파 유한 차분모형의 정확도를 향상시키기 위한 새로운 동시격자접속기법을 개발하였다. 이 격자접속기법은 공간에 대해 3차 보간식을 사용하므로 짧은 파에 대해서 보간에 따른 오차를 최소화할 수 있고, 시간에 대해 2차 보간식을 사용하기 때문에 기존 기법에 비해 더 정확한 값을 얻을 수 있다. 개발된 격자접속기법의 정확성을 평가하기 위해 수중 원형천퇴상을 전파하는 Gaussian 형상의 가상지진에 대해 격자접속기법을 적용하지 않고 계산한 결과와 격자접속기법을 적용하여 계산한 결과를 FUNWAVE에 포함되어 있는 선형화된 Boussinesq방정식에 의해 계산된 수치해와 비교하였다. 그 결과 개발된 동시격자접속기법의 우수함이 검증되었다.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.17 no.3
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• pp.202-212
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• 2005

In the design of an of offshore structure located near an underwater shoal, the same amount of attention given to the wave height may have to be put to the wave induced current as well since some of the wave energy translates to the current. In the present study, two numerical models each based on the nonlinear Boussinesq equation and the linear mild slope equation are applied to calculate the wave deformation and secondly induced current around a shoal. The underwater shoal in Vincent and briggs' experiment (1989) is used here, and all non-breaking wave conditions of the experiment with various monochromatic and unidirectional or multidirectional spectral wave incidences are concerned. Both numerical models clearly showed wave induced currents symmetrically farmed along the centerline over the shoal. The calculated wave heights along a preset line also generally showed very nice agreements with the experimental values.

• Journal of Korea Water Resources Association
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• v.38 no.6 s.155
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• pp.429-438
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• 2005

In this study, a couple of ordinary differential equations which can describe random waves are derived from the Boussinesq equations. Incident random waves are generated by using the TMA(TEXEL storm, MARSEN, ARSLOE) shallow-water spectrum. The governing equations are integrated with the 4-th order Runge-Kutta method. By using newly derived wave equations, nonlinear energy interaction of propagating waves in constant depth is studied. The characteristics of random waves propagate over a sinusoidally varying topography lying on a sloping beach are also investigated numerically. Transmission and reflection of random waves are considerably affected by nonlinearity.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.18 no.2
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• pp.166-177
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• 2006

The accuracy impact of using high-order Boussinesq-type model as compared to the typical order model is examined in this paper. The multi-layer model developed by Lynett and Liu(2004a) is used for simulating of wave breaking over a shelf region. The nonlinearity of the waves tested, ${k_0}{A_0}$, ranges from 0.029 to 0.180. The overall agreement between the two-layer model and the hydraulic experiments are quite good. The one-layer model overshoals the wave near the breakpoint, while the two-layer model shoals at a rate more consistent with the experimental data.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.18 no.2
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• pp.154-165
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• 2006

In the present study, a numerical model using Boussinesq equation is set up to predict the interacted equilibrium between waves and their induced currents in the occurrence of breaking waves over an underwater shoal, and the numerical results are compared with results of existing hydraulic experiments. A sensitivity analysis has been done to find out appropriate values of breaking wave parameters with the result (regular wave case) of Vincent and Briggs (1989)’ experiment. Then the numerical model is applied to the irregular wave cases of the experiment and the hydraulic model test of Ieodo which is a natural undersea shoal. The results show that a strong current forms in the wave direction at the downstream side of the shoals, causing the attenuation of wave heights there. The calculated wave heights generally show a similar pattern with the measured data.